Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles

Abstract

Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.

arXiv comment14+7 pages, 2 figures

References in corpus (38)

• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Braiding statistics approach to symmetry-protected topological phases
• The effects of interactions on the topological classification of free fermion systems
• Coupling a QFT to a TQFT and Duality
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Complete classification of 1D gapped quantum phases in interacting spin systems
• A classification of symmetry enriched topological phases with exactly solvable models
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Anomalies of discrete symmetries in three dimensions and group cohomology
• A theory of 2+1D bosonic topological orders
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Topological invariants for gauge theories and symmetry-protected topological phases
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
• Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Chiral symmetry on the edge of 2D symmetry protected topological phases
• Loop braiding statistics in exactly soluble 3D lattice models
• Symmetry protected topological orders of 1D spin systems with D2+T symmetry
• Chern-Simons Field Theories with Non-semisimple Gauge Group of Symmetry

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• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
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• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
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• Wilson operator algebras and ground states for coupled BF theories
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• Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions
• Entanglement entropy of (3+1)D topological orders with excitations
• Anomalies and entanglement renormalization
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids
• Non-Abelian Fusion, Shrinking and Quantum Dimensions of Abelian Gauge Fluxes
• Fractionalizing Global Symmetry on Looplike Topological Excitations
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Continuum field theory of 3D topological orders with emergent fermions and braiding statistics
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• A new strategy to microscopic modelling of topological entanglement in polymers based on field theory
• Multi-flavor string-net models
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• Intertwined order of generalized global symmetries
• Universal fault tolerant quantum computation in 2D without getting tied in knots